My roughly-sketched idea:
You need an ATF-issued license to own a gun, which entails passing background and mental health checks, and also passing a written and/or demonstrated safety exam. You have to go to an ATF-run facility every 3-5 years to renew your gun ownership license, which may involve retesting or re-background checking. And you have to bring your registered guns with you. If you don't show up, or don't produce all your guns, you lose your license, and a warrant can be issued to confiscate your guns. You can only resell to strictly-licensed gun dealers (not every corner pawn shop), and all sales must be registered or you and the buyer both lose your license. The government will always buy back your gun at market value. If you report too many guns as "lost" or "stolen," you lose your license.
As for the guns themselves, I'd like to see technology knocked back like 100 years. Handguns have to be revolvers, rifles have to be bolt- or lever-action, shotguns have to be pumped. No type can hold more than 6 rounds.
/end pipe dream